On this slide, we show a schematic of a rocket engine.
In a
rocket engine,
stored fuel and stored oxidizer
are ignited in a combustion chamber.
The combustion produces great amounts of exhaust gas at high
temperature
and
pressure.
The hot exhaust is passed through a
nozzle
which accelerates the flow.
Thrust
is produced according to Newton's
third law
of motion.

The amount of thrust produced by the rocket depends
on the mass flow rate through the engine, the exit
velocity of the exhaust, and the pressure at the nozzle
exit. All of these variables depend
on the design of the nozzle.
The smallest cross-sectional area of the nozzle is called the
throat of the nozzle. The hot exhaust flow is
choked
at the throat, which means that the
Mach number
is equal to 1.0 in the throat and the
mass flow ratem dot
is determined by the throat area.
The area ratio from the throat
to the exit Ae sets the
exit velocityVe
and the exit pressure pe.
You can explore the design and operation of a rocket nozzle with our
interactive thrust simulator
program which runs on your browser.

The exit pressure is
only equal to free stream pressure at some design condition.
We must, therefore, use the longer version of the generalized
thrust equation
to describe the thrust of the system.
If the free stream pressure is given by p0,
the thrust F equation becomes:

F = m dot * Ve + (pe - p0) * Ae

Notice that there is no free
stream mass times free stream velocity term
in the thrust equation
because no external air is brought on board. Since the oxidizer is
carried on board the rocket, rockets can generate thrust in a vacuum
where there is no other source of oxygen. That's why a rocket will
work in space, where there is no surrounding air,
and a
gas turbine
or
propeller
will not work.
Turbine engines and propellers rely on the atmosphere to provide
air as the working fluid for propulsion and oxygen in the air
as oxidizer for combustion.

The thrust equation shown above works for both
liquid rocket
and
solid rocket.
engines.
There is also an efficiency parameter called the
specific impulse
which works for both types of rockets and greatly simplifies
the performance analysis for rockets.